Question

A fish is 11.9 cm from the front surface of a fish bowl of radius 33 cm. Where does the fish appear to be to someone in air viewing it from in front of the bowl

Answer 1

The fish would appear 42.7 cm on the left side from the front of the bowl.

Step-by-step explanation:

The fish (object) distance = 11.9 cm, radius of curvature of the bowl = 33 cm. The distance of image of the fish (image distance) can be determined by applying the mirror formula;

`(1)/(f)` =
`(1)/(u)` +
`(1)/(v)`

where f is the focal length of the reflecting surface, u is the object distance and v is the image distance.

But, f =
`(radius of curvature)/(2)`

=
`(33)/(2)`

f = 16.5 cm

Substitute f = 16.5 =
`(165)/(10)`, and u = 11.9 =
`(119)/(10)` in equation 1;

`(10)/(165)` =
`(10)/(119)` +
`(1)/(v)`

`(1)/(v)` =
`(10)/(165)` -
`(10)/(119)`

=
`(1190 - 1650)/(19635)`

`(1)/(v)` =
`(-460)/(19635)`

⇒ v =
`(19635)/(-460)`

= -42.6848

v = 42.7 cm

The fish would appear 42.7 cm on the left side from the front of the bowl.